The sums of the four combinations of three of four numbers

Question

The sums of the four combinations of three of four numbers are 88, 69, 103, and 76. What is the largest of the four numbers ?

(A) 40
(B) 41
(C) 42
(D) 43
(E) 44

adconsectetur · Answer

Sum = 336/3 = 112

Sum of three smallest = 69.

Largest = 112 - 69 = 43

Hope it helps

Priyanshu7297 · Answer

Can you please explain the question first because it's hard to understand what the question is asking

Tinytrotter · Answer

So the question is providing information about 4 numbers - let us assume them as a, b, c & d. The question tells us that the combinations of 3 numbers which can be made out of these 4 i.e. 4C3 = 4 combinations have the sum as 69, 76, 88 & 103 which basically means for example: a+b+c = 69, a+c+d = 76 and so on.

We need to find the largest number. For ease of solving, let us assume A<B<C<D i.e. we need to find D.

If we add up all the 4 sums provided to us, we get 3A + 3B + 3C + 3D = 336 i.e. 3 (A + B + C + D) = 336 i.e. A + B + C + D = 112. Now because we have assumed A<B<C<D, we know that A + B + C is the smallest sum possble which is 69. Therefore 69 + D = 112 i.e. D = 43.

Adit_ · Answer

I don't think assuming that one is greater than the other is prudent here. Answer is right but there can be a scenario where it doesn't hold true IMO.

Best way is to add them all up first.
You will get 3(a+b+c+d) = 336.
So a+b+c+d = 112.

Now to get the individual numbers simply subtract this total sum by each of the sums.
If a+b+c = 88, if you chose, then d = 112-88 = 24.
So on you can find the remaining numbers as well.

vasu1104 · Answer

total numbers= 4 
say 4 numbers are a,b,c,d.
we need to first find four combinations of 3 numbers from those 4 numbers.

the combinations are a+b+c, a+b+d, b+c+d, c+d+a.
the sums of each of these are 88,69,103,76.

now if we add all these together, we get 3(a+b+c+d) = 336
a+b+c+d = 112

but we dont know exactly which combinations represents any of this sum.
so just say a+b+c = 88

now if put the sum of a+b+c into a+b+c+d, we get d=24

say a+b+d = 69
from here we get a+b = 45

now we are left with last two sum combinations.
say b+c+d = 103 and c+d+a = 76
when we add this two, we get = 2c+2d+a+b = 179.
we know a+b = 45. use that and we can find c+d.
2(c+d)+45 = 179
2(c+d) = 134
c+d = 67
we know d=24. so c= 43

so we got value of c and d. lets find a and b and then we can see largest value.
we have b+c+d= 103
so b= 36

also c+d+a = 76.
so a = 9

now a=9, b = 36, c = 43, d = 24

so largest value C = 43

so choice D

The sums of the four combinations of three of four numbers

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The sums of the four combinations of three of four numbers

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